Ground-state properties and elementary excitations of quantum droplets in dipolar Bose-Einstein condensates

Abstract

Recent experiments have revealed the formation of stable droplets in dipolar Bose-Einstein condensates. This surprising result has been explained by the stabilization given by quantum fluctuations. We study in detail the properties of a BEC in the presence of quantum stabilization. The ground-state phase diagram presents three main regimes: mean-field regime, in which the quantum correction is perturbative, droplet regime, in which quantum stabilization is crucial, and a multistable regime. In the absence of a multi-stable region, the condensate undergoes a crossover from the mean-field to the droplet solution marked by a characteristic growth of the peak density that may be employed to clearly distinguish quantum stabilization from other stabilization mechanisms. Interestingly quantum stabilization allows for three-dimensionally self-bound condensates. We characterized these self-bound solutions, and discuss their realization in experiments. We conclude with a discussion of the lowest-lying excitations both for trapped condensates, and for self-bound solutions.

Quantum dilute droplets of dipolar bosons at finite temperature

“…A similar mechanism has been recently proposed to stabilize droplets in attractive Bose-Bose mixtures [38]. These dipolar droplets remain stable even in the absence of external harmonic confinement, forming self-bound ensembles [37,39,40]. Most recently, the observation of a macro-droplet state in an ultracold bosonic gas of erbium atoms with strong dipolar interactions has been reported by the Innsbruck team [41].…”

Ground state of an ultracold Fermi gas of tilted dipoles in elongated traps

“…Nevertheless, if the DDI is weak enough, as in the case of erbium atomic gases, the difference between the ballistic (free) and non-ballistic expansion is small, as already shown in [46]. Thus, (27) can approximately be used in our case and the value of A K in global equilibrium can be extracted from the long-time limit of A R , which is available from the experimental data. We highlight that in some limiting cases it is still possible to take into account a non-ballistic expansion by using the previously developed dynamical theory [46].…”

“…Therefore, we conclude that the agreement of experimental data and theoretical results in figure 8(a) can be further improved by developing a theory for a non-ballistic expansion for a general experiment geometry, which is out of the scope of the present study. Figure 8(b) shows a comparison of our theoretical and experimental results for the deformation Δ of the FS for the three considered cases, where the experimental values are calculated according to (26), assuming ballistic expansion (27) and using the real-space aspect ratios shown in figure 8(a). Although the statistical error bars A R exp D for the experimentally measured values of the real-space aspect ratios are small and almost constant, the corresponding errors for the FS deformation, calculated as…”

Two-dimensional quantum droplets in dipolar Bose gases

“…One of the most fascinating phenomena recently observed in dipolar Bose-Einstein condensates (BEC) with Dy and Er atoms is the formation of self-bound droplets [1][2][3][4]. Theoretically, a wealth of studies have been spawned for highlighting the behavior of droplet states [5][6][7][8][9][10][11][12][13][14]. These so-called liquid droplets are stable even in the absence of external trapping [3,8,9] (self-bound) due to the competition between attraction, repulsion and Lee-Huang-Yang (LHY) quantum fluctuations [15][16][17].…”